> This restricts us from looking at one of the cutest adjunction constructions I know. If we have a Monad m, we compute two adjunctions! It's a classic construction. I don't think it's in Fong and Spivak It is at the heart of the >=> operator in Haskell if you've ever used it.
I understand >=> to be composition of morphisms in the Kleisli category of the relevant monad. But how does >=> relate to adjunctions?